Second Cox processes with \(\eta \)  to be an additive process or
subordinator are regarded as random time changes of Lévy processes and these Cox
processes are known to have independent (and stationary) increments (see
[1]}, [2]}, [3]}). Therefore we obtain a kind of reverse result,
i.e. assuming independent (and stationary) increments of the time
changed non-negative additive or Lévy processes, we show that the underlying
process should be a subordinator.
